Question

How do you solve `\sqrt { 3x - 2} + 4= 8`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(4)` from each side of the equation to isolate the radical while keeping the equation balanced:

`sqrt(3x - 2) + 4 - color(red)(4) = 8 - color(red)(4)`

`sqrt(3x - 2) + 0 = 4`

`sqrt(3x - 2) = 4`

Next, square both sides of the equation to eliminate the radical while keeping the equation balanced:

`(sqrt(3x - 2))^2 = 4^2`

`3x - 2 = 16`

Then, add `color(red)(2)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`3x - 2 + color(red)(2) = 16 + color(red)(2)`

`3x - 0 = 18`

`3x = 18`

Now, divide each side of the equation by `color(red)(3)` to solve for `x` while keeping the equation balanced:

`(3x)/color(red)(3) = 18/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 6`

`x = 6`